## anonymous 5 years ago Find all the values of x in the interval [0, 2pie] that satisfy the equation 2cos(x) + sin(2x) = 0.

1. anonymous

step one is to rewrite $sin(2x)=2sin(x)cos(x)$

2. anonymous

then you get $2cos(x)+2cos(x)sin(x)=0$ $2cos(x)(1+sin(x))=0$ $cos(x)=0$ or $1+sin(x)=0$ $sin(x)=-\frac{1}{2}$

3. anonymous

can you solve from there?

4. anonymous

5. anonymous

sure. you are in the interval $(0,2\pi)$

6. anonymous

in that interval cosine is 0 at $\frac{\pi}{2}$ and $\frac{3\pi}{2}$

7. anonymous

are those fractions?

8. anonymous

if you do not instantly know where $sin(x)=-\frac{1}{2}$ then look at the cheat sheet http://tutorial.math.lamar.edu/cheat_table.aspx and see that it is at $\frac{7\pi}{6}$ and $\frac{11\pi}{6}$

9. anonymous

that is where the second coordinate is $-\frac{1}{2}$

10. anonymous

unit circle on last page of cheat sheet